Coupling-function formulation for monodisperse spray diffusion flames with infinitely fast chemistry

Abstract

A general formulation is given for the numerical computation of spray diffusion flames in the Burke–Schumann limit of infinitely fast chemical reaction, with nonunity Lewis numbers allowed for the different reactants. Linear combinations of the conservation equations for the species and energy are used to formulate the gas-phase problem in terms of chemistry-free coupling functions. The resulting set of gas-phase conservations equations, which include homogenized source terms associated with the force acting on and the heating and vaporization of the droplets, are accompanied by a Eulerian description of the liquid phase, with appropriate conservation equations written for the number density, velocity, temperature, and radius of the droplets in the limiting case of small values of the volume fraction occupied by the droplets. The resulting formulation can be used in direct numerical simulations of spray diffusion flames and may also serve as a starting point in modeling strategies of turbulent flows. It is employed here for analysis of the combustion of a typical hollow-cone spray issuing from a pressure-swirl atomizer.